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In this paper we show there are no classical type simple Lie 2-algebras withtoral rank odd and we also show that the simple contragredient Lie 2-algebra$G(F_{4, a})$ of dimension 34 has toral rank 4, and we give the Cartandecomposition of $G(F_{4, a})$.

Classical simple Lie 2-algebras of toral rank 3 and a contragredient Lie 2-algebra of toral rank 4